Magnetic order and electromagnon excitations in ${\mathrm{DyMnO}}_3$ studied by neutron scattering experiments

Magnetic order and excitations in multiferroic ${\mathrm{DyMnO}}_3$ were studied by neutron scattering experiments using a single crystal prepared with an enriched ${}^{162}\mathrm{Dy}$ isotope. The ordering of Mn moments exhibits pronounced hysteresis arising from the interplay between Mn and Dy magnetism, which has a strong impact on the ferroelectric polarization. The magnon dispersion resembles that reported for ${\mathrm{TbMnO}}_3$. We identify the excitations at the magnetic zone center and near the zone boundary in the $b$ direction, which can possess electromagnon character. The lowest frequency of the zone-center magnons is in good agreement with a signal in a recent optical measurement, so this mode can be identified as the electromagnon coupled by the same Dzyaloshinskii-Moriya interaction as the static multiferroic phase.

Figure 1

Illustration of polarization patterns of several magnon modes which are relevant for the discussion of electromagnons in ${\mathrm{DyMnO}}_3$. In all parts the static cycloid is shown by large blue arrows rotating in the cycloid plane indicated by the shaded circles. The propagation vector of the modulation in $b$ corresponds to that in ${\mathrm{DyMnO}}_3$ with two Mn atoms per layer and unit cell. (a) The pattern of the phason mode at the magnetic zone center. The frozen-in oscillating displacements of the spins are indicated by the small green arrows. Adapting the inverse Dzyaloshinskii-Moriya interaction described by Eq. (1) does not result in an oscillating polarization because the cross product $({\vec{S}}_i\times {\vec{S}}_j)$ is constant. (b) The CRM associated with the rotation of the entire cycloid around the $b$ direction. In this mode the spin cross product and thus the electric polarization rotate around $b$ so that there is an oscillating polarization along $a$ which can couple with electromagnetic radiation with $\vec{E}$ parallel to $a$. (c) The HM in which the spiral plane rotates around the $c$ axis, modifying the character of the spiral from a pure cycloid to a partially helical one. Applying Eq. (1) will yield only a quadratic coupling with the electric polarization. (d) The polarization of the mode polarized within the cycloid plane $(b,c$ plane) appearing at the propagation vector with the $k$ component $k_{\mathrm{elm}-\mathrm{str}}=1-k_{\mathrm{inc}}=0.64$. This mode gains a strong oscillating electric polarization through the exchange striction mechanism. In the static cycloid the scalar product $\overrightarrow{S_i}·\overrightarrow{S_j}$ is constant; its momentous deviation from the average value is indicated by the vertical magenta bars.

Figure 2

Temperature dependence of the magnetic $\left(0k1\right)$ reflection measured from an isotopically enriched ${\mathrm{DyMnO}}_{\text{3}}$ single crystal. Data were collected on the 4F2 spectrometer upon cooling and heating (counting time of $\sim 60$ s); note the different peak positions observed even far above the ordering temperature of Dy moments.

Figure 3

Temperature dependence of elastic magnetic scattering in ${\mathrm{DyMnO}}_{\text{3}}$ at $\left(0k1\right)$ studied on the 1T spectrometer upon (top) cooling and (bottom) heating. At fixed temperatures the scattering intensity was recorded by scanning along $\left(0k1\right)$. The color coding corresponds to a logarithmic scale for a counting time of about 15 s; note that the lower scans extend to larger $k$ values.

Figure 4

Temperature dependence of elastic magnetic $\left(0k1\right)$ scattering in ${\mathrm{DyMnO}}_{\text{3}}$ studied on the 1T spectrometer upon cooling and heating. The $\left(0k1\right)$ scans shown in Fig. 3 were fitted by one or two Lorentzian peak profiles (see Fig. 3). (a) The peak intensity (height) of the strongest peak as a function of temperature; the inset displays the height of the (0 0.5 1) peak that is associated with the ordering of Dy moments upon cooling (solid circles) and heating (open circles). (b) The incommensurate pitch (peak position) of the strongest signal; at low temperatures (open circles) the measured profiles were fitted with two Lorentzians. The inset displays an enlargement of the temperature range near 18 K corresponding to the onset of ferroelectric order. (c) The temperature dependence of the FWHM of the fitted peak profiles, which senses the impact of the Dy ordering.

Figure 5

(a) Constant $\vec{Q}$ scans to determine the low-energy magnetic excitations between $\vec{Q}=\left(00.3631\right)$ and (0 0 1) and dispersion. Slightly above an energy of 3 meV some signal may arise from a Dy crystal-field excitation of the lifting of Kramer's doublet degeneracy. (b) The flat dispersion in this part of the Brillouin zone.

Figure 6

Constant $\vec{Q}$ scans taken at various point in the Brillouin zone to establish the magnon dispersion in ${\mathrm{DyMnO}}_{\text{3}}$: (a) magnetic zone center, (b) end point of the dispersion in the $b$ direction, and the zone boundary in the $c$ direction (c) with and (d) without the incommensurate modulation along $b$.

Figure 7

Dispersion of magnetic excitations along the $b$ direction shown as a color contour plot of the scattered intensities. The lines denote the spin-wave dispersion calculated with linear theory as described in Ref. [43]. Parameters were $J_{\mathrm{FM}}=0.12$ meV (0.14 meV), $J_{\mathrm{AFM}}=-0.4$ meV $(-0.35$ meV), and $\Lambda =0.19$ meV (0.4 meV) for the lower (upper) curve; red dots denote peak positions determined by fitting Gaussians to the measured scans.

Figure 8

Temperature dependence of electromagnons in ${\mathrm{DyMnO}}_{\text{3}}$. The inelastic neutron scattering results (red squares) are compared with those of spectroscopic measurements [5] (black circles) for the lowest mode. Lines are guides to the eye.